2014/02（追試）
Counting Systems: Where Do They Come From?
(1) Have you ever counted a large number of items such as paper clips or postcards? Most likely, you first separated them into smaller piles of ten each and then counted the piles. By doing so, you were using the number 10 as the unit for your calculation, a counting system referred to as the base-10 system. In fact, most people around the world count using the base-10 system, a method which scholars say we probably inherited from early ancestors who counted, quite naturally, with their fingers. Because this approach seems so familiar, you may think that counting with 10 is universal. However, if we look at the world around us, other counting systems are not very hard to find.
(2) The watch on your wrist or the clock on a nearby wall is probably as far as you need to go to find a different counting system. An hour can be divided into 60 minutes, and a minute is made up of 60 seconds. Ancient Mesopotamians, whose system of time we have adopted, are believed to have used a base-60 system. The Mesopotamian year was divided into 360 days, so the base-60 system fit very well into their calendar. Moreover, the number 60 can be divided into many different equal amounts. The divisions on the face of a clock include two thirty-minute periods, four fifteen-minute periods, six ten-minute periods, and twelve five-minute periods. While 60 might seem like an unusual choice for a base, it works well for measuring time.
(3) Every time you use a computer, you are relying on one of the most important numerical tools in the modern world: the base-2 system. In this binary system, only two digits, 0 and 1, are used; combinations of these numbers are used to represent larger numbers. One reason the base-2 system was chosen is that the “digital switches” inside the computer can be set to either ON or OFF, represented by 1 and 0, respectively. It is relatively easy to construct a machine that makes a distinction between only two choices. The base-10 system, on the other hand, would make computer engineering much more complicated.
(4) As you can see, different ways of thinking inspire different counting systems. One unique example relates to the speakers of Northern Pame, a language spoken in Mexico. Whereas you might separate candies or books into piles of ten, the Northern Pame-speaking people would make piles of eight. As with the base-10 system, the reason they have adopted a base-8 system is a somatic one. Instead of counting their fingers, however, they count the eight spaces between their fingers. Although Mexico today is a base-10 country, this group of over 5, 000 people continues to use the number 8 as the base for everyday counting.
(5) All these counting systems have emerged from people’s understanding of the world around them. However, sometimes a government steps in and establishes a system for its citizens. For example, Britain once used a complicated counting system for its currency units; 1 pound equaled 20 shillings, but 1 shilling equaled 12 pennies. This system had developed over hundreds of years as a result of political and commercial situations. In 1966, the government announced that the country would be switching to a base-lO system for their currency five years later. Shops prepared charts to help the customers understand the new coins and bills, and the transition to the new system was relatively smooth.
(6) Throughout history, we humans have worked to understand, organize, and describe the world around us. Each culture has done so in its own unique way, developing systems that reflect the physical characteristics of humans, their needs and desires, and their environment. As we have seen here, the various counting systems people have invented are an excellent example of this. The fact that there is no universal counting system, but a number of systems appropriate to specific situations, is proof of how creative and flexible we are.
- In paragraph (2), the author tells us that
① ancient Mesopotamians believed the base-60 system was unusual
② clock faces could be improved if the base-10 system were adopted
③ the base-60 system did not appear in human history until recently
④ the base-60 system is highly convenient for measuring time - In paragraph (3), the author explains that
① computers can be more easily operated with the base-2 system
② each digital computer switch can distinguish several numbers
③ the base-10 system suits the electrical qualities of computers
④ the binary system is quite demanding in computer engineering - In paragraph (4), the word somatic means
① related to psychology
② related to technology
③ related to the body
④ related to the environment - According to paragraph (5), which of the following statements is true?
① 1971 was the first time that the British currency system changed.
② British people adopted the new system with no major problems.
③ British people complained about the charts prepared by the shops.
④ The British government failed to introduce a base-10 currency system. - The author’s main point in paragraph (6) is that
① a universal counting system may be established in the future
② counting systems are mainly decided by our body features
③ humans have adapted counting systems to the world around them
④ most cultures have similar environmental conditions and needs
